A behavioural approach to the pricing of European options

Empirical studies on quoted options highlight deviations from the theoretical model of Black and Scholes; this is due to different causes, such as assumptions regarding the price dynamics, markets frictions and investors’ attitude toward risk. In this contribution, we focus on this latter issue and study how to value options within the continuous cumulative prospect theory. According to prospect theory, individuals do not always take their decisions consistently with the maximization of expected utility. Decision makers have biased probability estimates; they tend to underweight high probabilities and overweight low probabilities. Risk attitude, loss aversion and subjective probabilities are described by two functions: a value function and a weighting function, respectively. As in Versluis et al. [15], we evaluate European options; we consider the pricing problem both from the writer’s and holder’s perspective, and extend the model to the put option. We also use alternative probability weighting functions

Systematic factors, information release and market volatility

Recent several months have demonstrated historical levels of market volatility; sometimes attributed to changes in previously hypothesized systematic risk factors, however many times without any known reason other than the overreaction by market participants. Times like these make it even more important that we have a better understanding of how markets receive and evaluate new information about systematic risk factors such as macroeconomic variables. Despite a strong intuitive notion and established theoretical relationships that these risk factors should influence equity values, few studies have been able to establish this relationship empirically. Previous research has used cash-market prices for equity indices, but perhaps options on those indices are more sensitive to the new information released to the market by the announcement of macroeconomic variables, as suggested by numerous empirical studies supporting the hypothesis that option traders might be a better informed segment of the population. In this study, I examine the impact of a broad set of macroeconomic announcements on equity index options, in search of candidates for priced factors. The data set includes 19 macro announcement series and daily option prices for the period from 1983 to 2002. I find that balance of trade, consumer price index, producer price index, employment, housing starts, money supply and retail sales are associated with higher volatility of index option returns.

European option pricing under cumulative prospect theory with constant relative sensitivity probability weighting functions

In this contribution, we evaluate European financial options under continuous cumulative prospect theory. In prospect theory, risk attitude and loss aversion are shaped via a value function, while a probability weighting function models probabilistic risk perception. We focus on investors’ probability risk attitudes, as probability weighting may be one of the possible causes of the differences between empirically observed options prices and theoretical prices obtained with the Black and Scholes formula. We consider alternative probability weighting functions; in particular, we adopt the constant relative sensitivity weighting function, whose parameters have a direct interpretation in terms of curvature and elevation. Curvature models optimism and pessimism when one moves from extreme probabilities, whereas elevation can be interpreted as a measure of relative optimism. We performed a variety of numerical experiments and studied the effects of these features on options prices and implied volatilities